To　characterize　the　influence　of　randomness　of　ground　motion　on　the　pounding　separation　distance,　based　on　the　stochastic　vibration　theory　and　the　matrix　system　reliability　computing　method,　a　probabilistic　approach　was　proposed　to　evaluate　the　required　separation　length　of　a　bridge　system.　Firstly,　a　probability　model　was　developed　on　pounding　separation　distance　of　a　bridge　under　spatially　varying　seismic　loads.　Secondly,　the　finite　element　model　of　the　bridge　pounding　system　was　built,　and　the　conditional　exceedance　probability　relation　of　the　separation　distance　between　the　adjacent　bridge　decks　and　the　earthquake　magnitude　was　obtained.　Finally,　by　using　the　matrix　system　reliability　computing　method,　the　pounding　probability　relation　of　the　bridge　system　and　separation　lengths　of　all　pounding　points　(deck-deck　and　deck-abutment)　was　obtained.　Some　important　conclusions　were　drawn　that　the　demand　of　the　separation　length　nonlinearly　increases　with　the　increase　in　the　magnitude;　the　demand　of　pounding　separation　distance　on　deck-abutment　at　two　ends　of　employed　bridge　was　almost　in　agreement　and　the　pounding　probability　at　deck-deck　pounding　point　was　about　20%　larger　than　that　at　deck-abutment　pounding　point.　At　a　magnitude　of　7,　the　probability　of　all　three　pounding　points　triggered　was　about　63%,　the　probability　of　at　least　two　collision　was　95%,　and　the　probability　of　at　least　one　collision　was　100%.　©　2018,　Engineering　Mechanics　Press.　All　right　reserved.